FIR Filter Design Research Articles

Multidimensional FIR Filter Design Via Trigonometric Sum-of-Squares Optimization

We discuss a method for multidimensional FIR filter design via sum-of-squares formulations of spectral mask constraints. The sum-of-squares optimization problem is expressed as a semidefinite program with low-rank structure, by sampling the constraints using discrete cosine and sine transforms. The resulting semidefinite program is then solved by a customized primal-dual interior-point method that exploits low-rank structure. This leads to a substantial reduction in the computational complexity, compared to general-purpose semidefinite programming methods that exploit sparsity.

Complex digital Laguerre filter design with weighted least square error subject to magnitude and phase constraints

Complex coefficient optimal digital Laguerre filter design with arbitrary asymmetric frequency response is developed. The optimization scheme is based on the weighted least square error criterion with complex Chebyshev error used as its magnitude and phase constraints. Developed version of the active set method has been exploited to solve the resultant semi-infinite quadratic programming problem. A quick and practical approach is proposed to evaluate the suboptimal value of the Laguerre parameter close to its optimum value. The design technique can be applied to design of asymmetric FIR filters just by setting the Laguerre parameter equal to zero. The accuracy of the processes has been verified by illustrating some numerical examples.

FIR Filter Design via Linear Complementarity Problem, Messy Genetic Algorithm, and Ising Messy Genetic Algorithm

FIR Filter Design via Linear Complementarity Problem, Messy Genetic Algorithm, and Ising Messy Genetic Algorithm

Digital transmit and receive linear phase matched filters

The relationship between the causal real symmetric pulse and the linear phase characteristic is used for matched filter design. Real symmetric pulse transmission leads to a linear phase pulse shaping filter which is matched at both the receiver and the transmitter ends. This provides the potential for inexpensive system on a chip (SOC) design since the hardware implementation for transmit and receive filter is similar. The discrete time delayed raised-cosine pulse is considered for the causal real symmetric Nyquist pulse. A novel pulse shaping filter that retains a raised-cosine shape in the impulse response rather than the frequency response is considered in this paper. This design is completely different than the typical raised-cosine filter where the raised-cosine shape is maintained in the frequency response. The raised-cosine pulse used in our design has a finite number of transmission zero pairs; therefore, it can be perfectly reconstructed as the unit-sample response of the filter. Consequently, the transfer function of the shaping filter is exactly obtained from the z-transform of the pulse. This digital filter can be used at the receiver after the power amplification stage to achieve the desired amplification linearity in constant amplitude modulation systems. FIR filter design examples for various values of the delay parameter are described, and bit error rate simulation is also provided.

Tuning of FIR filter transition bandwidth using fractional Fourier transform

The transition bandwidth of window-based FIR filters is proportional to the window main-lobe width, which in turn is proportional to the length of the window function. As such, transition bandwidth of FIR filters can be directly tuned by varying window length for on-line tuning applications. However, analysis of window functions in fractional Fourier domain, a generalization of Fourier domain, also establishes the dependence of window main-lobe width on the order of fractional Fourier transform (FRFT). Thus, an alternative methodology to tune the transition bandwidth, based on FRFT, is developed in this work. The proposed methodology is useful for frequency domain filtering and introduces a comparative ease in tuning by eliminating the need to re-compute the impulse response coefficients. Also, significant computational saving has been achieved using FRFT. However, it is observed that the direct approach can introduce a lot more adjustability in the transition bandwidth than the FRFT approach. Apart from Kaiser window, considered to be optimum for FIR filter design, another window with a high side-lobe fall-off-rate (SLFOR), viz, Parzen-cos 6 ( πt) (PC6), has also been used in the proposed on-line filter tuning. Better performance of windows with high SLFOR in on-line sharpening is illustrated with the aid of simulation results.

Linear phase FIR filter design using particle swarm optimization and genetic algorithms

In this paper, a linear phase FIR filter is designed using particle swarm optimization (PSO) and genetic algorithms (GA). Two design cases are considered. In the first case, the filter length, passband and stopband frequencies, and the ratio of the passband and stopband ripples size are specified. In the second case, a feasible passband and stopband ripples size in addition to the other three filter specifications are specified. The later situation is not explicitly considered by the Parks–McClellan (PM) algorithm. Furthermore, the PSO and the GA are used to design optimum FIR filters for which the filter coefficients are represented using finite word length. In all cases, the design goal is successfully achieved using the PSO and compared with that obtained using the GA. For the problem at hand, it is found that the PSO outperforms the GA in some of the presented design cases.

Least-Squares and Minimax Design of Polynomial Impulse Response FIR Filters for Reconstruction of Two-Periodic Nonuniformly Sampled Signals

This paper proposes polynomial impulse response finite-impulse response filters for reconstruction of two-periodic nonuniformly sampled signals. The foremost advantages of using these reconstruction filters are that on-line filter design thereby is avoided and subfilters with fixed dedicated multipliers can be employed in an implementation. The overall implementation cost can in this way be reduced substantially in applications where the sampling pattern changes from time to time. The paper presents two different design techniques that yield optimum filters in the least-squares and minimax senses, respectively. Design examples are included that illustrate the benefits of the proposed filters

Design of smallest size two-dimensional linear-phase FIR filters with magnitude error constraint

This paper presents an online procedure that produces the smallest feasible size of two-dimensional FIR filters with prescribed magnitude error constraint. The procedure uses the mean square normalized error of constrained and unconstrained least-square filters to produce the initial and the subsequent sizes that converge to the smallest feasible one in a few iterations, where the constrained least-square filters are defined as the least-square filters satisfying the magnitude error constraint. The procedure finally returns a smallest size filter that satisfies the magnitude error constraint and has least total squared magnitude error. Design examples of diamond-shaped, rectangular, and elliptic filters are provided, and comparisons with an exhaustive search are given.

Design of 2D FIR and IIR Digital Filters with Canonical Signed Digit Coefficients Using Singular Value Decomposition and Genetic Algorithms

In this paper a design approach for two-dimensional finite impulse and infinite impulse response digital filters with canonic signed digit (CSD) coefficients based on singular value decomposition and genetic algorithms (GAs) is presented. The proposed technique uses a new chromosome coding scheme to alleviate the problem encountered by many GAs during crossover and mutation which destroys the CSD property. Examples are given to demonstrate the usefulness of the proposed technique. A comparative study carried out with some of the existing techniques indicates the high throughput property of the proposed technique.

Design of FIR Digital Filters Using Hopfield Neural Network

This paper is intended to provide an alternative approach for the design of FIR filters by using a Hopfield Neural Network (HNN). The proposed approach establishes the error function between the amplitude response of the desired FIR filter and the designed one as a Lyapunov energy function to find the HNN parameters. Using the framework of HNN, the optimal filter coefficients can be obtained from the output state of the network. With the advantages of local connectivity, regularity and modularity, the architecture of the proposed approach can be applied to the design of differentiators and Hilbert transformer with significantly reduction of computational complexity and hardware cost. As the simulation results illustrate, the proposed neural-based method is capable of achieving an excellent performance for filter design.

Design of efficient multiplierless FIR filters

An algorithm for reducing the hardware complexity of linear phase finite impulse response digital filters that minimise the adder depth in the multiplier block adders (MBAs) is presented. The algorithm starts by aggressively reducing both the coefficient wordlength and the number of non-zero bits in the filter coefficients. This reduces the number of adders (the adder depth) that are needed to construct the coefficient multiplier and results in an increased operating frequency. A modification to the representation of the filter coefficients such that the number of full adders (FAs) in our hardware implementation is proportional to the product of the input signal wordlength and the number of adders is proposed. That is, in general, the number of FAs is independent of the coefficient wordlength and the number of shifts between non-zero bits in the coefficient. Results show that the proposed technique achieves a 67 and 70% reduction in the number of MBAs and the number of multiplier block FAs, respectively. A software program has been implemented, which generates a Verilog HDL description of the digital filter. The proposed technique is not limited to filters with only a small number of taps and has been successfully applied to filters with up to 500 taps.

Equalization of Loudspeaker and Room Responses Using Kautz Filters: Direct Least Squares Design

DSP-based correction of loudspeaker and room responses is becoming an important part of improving sound reproduction. Such response equalization (EQ) is based on using a digital filter in cascade with the reproduction channel to counteract the response errors introduced by loudspeakers and room acoustics. Several FIR and IIR filter design techniques have been proposed for equalization purposes. In this paper we investigate Kautz filters, an interesting class of IIR filters, from the point of view of direct least squares EQ design. Kautz filters can be seen as generalizations of FIR filters and their frequency-warped counterparts. They provide a flexible means to obtain desired frequency resolution behavior, which allows low filter orders even for complex corrections. Kautz filters have also the desirable property to avoid inverting dips in transfer function to sharp and long-ringing resonances in the equalizer. Furthermore, the direct least squares design is applicable to nonminimum-phase EQ design and allows using a desired target response. The proposed method is demonstrated by case examples with measured and synthetic loudspeaker and room responses.

Anti-image FIR filters for large interpolation factors

In this paper, the design of FIR filters using novel window families is introduced. These window functions are having high side-lobe-fall-off-rate (SLFOR). The designed filters can be used as anti-...

Design of Real FIR Filters With Arbitrary Magnitude and Phase Specifications Using a Neural-Based Approach

An efficient and yet simple neural-based approach is utilized to design real finite-impulse response filters with arbitrary complex frequency responses in the least-squares sense. The proposed approach establishes the quadratic error difference of the filter optimization in the frequency domain as the Lyapunov energy function. Consequently, the optimal filter coefficients are obtained with good performance and fast convergence speed. To achieve good convergences for large filter lengths, a cooling process of simulated annealing is used for the neural activation function. Several examples and comparisons to the existing methods are presented to illustrate the effectiveness and flexibility of the neural-based method

Broadband Beamspace DOA Estimation: Frequency-Domain and Time-Domain Processing Approaches

Frequency-domain and time-domain processing approaches to direction-of-arrival (DOA) estimation for multiple broadband far field signals using beamspace preprocessing structures are proposed. The technique is based on constant mainlobe response beam-forming. A set of frequency-domain and time-domain beamformers with constant (frequency independent) mainlobe response and controlled sidelobes is designed to cover the spatial sector of interest using optimal array pattern synthesis technique and optimal FIR filters design technique. These techniques lead the resulting beampatterns higher mainlobe approximation accuracy and yet lower sidelobes. For the scenario of strong out-of-sector interfering sources, our approaches can form nulls or notches in the direction of them and yet guarantee that the mainlobe response of the beamformers is constant over the design band. Numerical results show that the proposed time-domain processing DOA estimator has comparable performance with the proposed frequency-domain processing method, and that both of them are able to resolve correlated source signals and provide better resolution at lower signal-to-noise ratio (SNR) and lower root-mean-square error (RMSE) of the DOA estimate compared with the existing method. Our beamspace DOA estimators maintain good DOA estimation and spatial resolution capability in the scenario of strong out-of-sector interfering sources.

Design of a low-pass filter by multi-scale even order Gaussian derivatives

In this paper, a new low-pass FIR filter design technique for achieving variable stopband attenuation without altering the passband and stopband edges, is proposed. The filter function is a linear combination of multi-scale Gaussian derivatives. In the frequency domain, the spectral modes corresponding to the continuous Gaussian derivatives have monotonic tails. In discrete domain, this amounts to variable stopband attenuation which depends upon the truncation length of the continuous kernel, the ‘scale’ and the order of Gaussian derivatives. The proposed algorithm consists of derivation of some useful mathematical relations between the basic design parameters and the parameters of the Gaussian derivatives and an optimization technique that finally produces an equiripple passband lowpass FIR filter with a higher falloff rate at the beginning of the transition band. Such a filter with variable stopband attenuation may be effective at the time of reconstruction of the desired passband signal in a Σ– Δ modulator output.

Optimal design of complex FIR filters with arbitrary magnitude and group delay responses

This paper presents a method for the frequency-domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses. The method can deal with both the equiripple design problem and the peak constrained least squares (PCLS) design problem. Consequently, the method can also be applied to the equiripple passbands and PCLS stopbands design problem as a special case of the PCLS design. Both the equiripple and the PCLS design problems are converted into weighted least squares optimization problems. They are then solved iteratively with appropriately updated error weighting functions. A novel scheme for updating the error weighting function is developed to incorporate the design requirements. Design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods.

Introduction to digital signal processing and filter design

Preface. 1. Introduction. 1.1 Introduction. 1.2 Application of DSP. 1.3 Discrete-Time Signals. 1.4 History of Filter Design. 1.5 Analog and Digital Signal Processing. 1.6 Summary. Problems. References. 2. Time-Domain Analysis and z Transform. 2.1 A Linear, Time-Invariant System. 2.2 z Transform Theory. 2.3 Using z Transform to Solve Difference Equations. 2.4 Solving Difference Equations Using the Classical Method. 2.5 z Transform Method Revisited. 2.6 Convolution Revisited. 2.7 A Model from Other Models. 2.8 Stability. 2.9 Solution Using MATLAB Functions. 2.10 Summary. Problems. References. 3. Frequency-Domain Analysis. 3.1 Introduction. 3.2 Theory of Sampling. 3.3 DTFT and IDTFT. 3.4 DTFT of Unit Step Sequence. 3.5 Use of MATLAB to Compute DTFT. 3.6 DTFS and DFT. 3.7 Fast Fourier Transform. 3.8 Use of MATLAB to Compute DFT and IDFT. 3.9 Summary/ Problems. References. 4. Infinite Impulse Response Filters. 4.1 Introduction. 4.2 Magnitude Approximation of Analog Filters. 4.3 Analog Frequency Transformations. 4.4 Digital Filters. 4.5 Impulse-Invariant Transformation. 4.6 Bilinear Transformation. 4.7 Digital Spectral Transformation. 4.8 Allpass Filters. 4.9 IIR Filter Design Using MATLAB. 4.10 Yule-Walker Approximation. 4.11 Summary. Problems. References. 5. Finite Impulse Response Filters. 5.1 Introduction. 5.2 Linear Phase Fir Filters. 5.3 Fourier Series Method Modified by Windows. 5.4 Design of Windowed FIR Filter Using MATLAB. 5.5 Equiripple Linear Phase FIR Filters. 5.6 Design of Equiripple FIR Filters Using MATLAB. 5.7 Frequency Sampling Method. 5.8 Summary. Problems. References. 6. Filter Realizations. 6.1 Introduction. 6.2 FIR Filter Realizations. 6.3 IIR Filter Realizations. 6.4 Allpass Filters in Parallel. 6.5 Realization of FIR and IIR Filters Using MATLAB. 6.6 Summary. Problems. References. 7. Quantized Filter Analysis. 7.1 Introduction. 7.2 Filter Design-Analysis Tool. 7.3 Quantized Filter Analysis. 7.4 Binary Numbers and Arithmetic. 7.5 Quantization Analysis of IIR Filters. 7.6 Quantization Analyis of FIR Filters. 7.7 Summary. Problems. References. 8. Hardware Design Using DSP Chips. 8.1 Introduction. 8.2 Simulink and Real-Time Workshop. 8.3 Design Preliminaries. 8.4 Code Generation. 8.5 Code Composer Studio. 8.6 Simulator and Emulator. 8.7 Conclusion. References. 9. MATLAB Primer. 9.1 Introduction. 9.2 Signal Processing Toolbox. References. Index.

Design of Equiripple Minimum Phase FIR Filters with Ripple Ratio Control

In this paper, we present a numerical method for the equiripple approximation of minimum phase FIR digital filters. Many methods have been proposed for the design of such filters. Many of them first design a linear phase filter whose length is twice as long, and then factorize the filter to obtain the minimum phase. Although these methods theoretically guarantee its optimality, it is difficult to control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by trial and error to achieve the ratio of the weights exactly. To address this problem, we modifies well-known Parks-McClellan algorithm and make it possible to directly control the ripple ratios. The method iteratively solves a set of linear equations with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.

Design of narrowband frequency sampling FIR filters using Z-window

In this work a method for automatic design of narrowband frequency sampling low-pass digital FIR filters is presented. Spectral response of Zhong (Z)-window has been used to provide the filtering action. Z-windows are used as variable windows by varying the side-lobe dip position. The proposed design methodology is a hybridization of the concepts of frequency sampling method and window method of filter design. This proposed design technique produces low-pass FIR filters featuring sharp cut off, exactly marked pass-band and cut off frequencies along with tolerable pass-band ripple and variable stop-band attenuation. For the filter applications requiring brick-wall response, considerable saving in the filter order can be achieved with subsequent reduction in computational and storage requirements by this method.